WHICH WAYS OF COOKING MEAT AND MILK DOES THE TORAH FORBID? [Basar v'Chalav :cooking ]
Gemara
(Mishnah): If one used the skin of the stomach to curdle milk, it is permitted;
If the milk absorbed the taste of meat, it is forbidden.
97b (Shmuel): Salting is like Rose'ach (boiling hot). Pickling is like cooking.
(Rav Acha): Since he said that pickling is like cooking, we infer that salting is not. Rather it is like roasting.
Avodah Zarah 35a (Shmuel): Chachamim forbade cheese of Nochrim because they curdle the milk in the skin of stomachs of Neveilos.
Question: Rav Chisda and Rav Nachman bar Yitzchak say that they use vinegar or sap of Orlah to curdle. If so, the cheese should be Asur b'Hana'ah!
Sanhedrin 4a (Rav Acha bar Yakov): Surely, all the Tana'im expound the way we pronounce a verse!
Support (Beraisa) Suggestion: Perhaps "ba'Chalev Imo" forbids cooking meat in Chelev (intestinal fats)!
Rejection: We learn (only) from the way we read it (milk. No Tana forbids cooking meat in Chelev.)
Rejection: "Lo Sevashel Gedi ba'Chalev Imo" - the Torah forbade the way of cooking. (This applies to milk, but not to Chelev.)
Pesachim 41a (Beraisa - Rebbi) "U'Vashel Mevushal" forbids cooking the Pesach in liquids other than water.
This forbids also Tzeli Kedar (cooking it in a pot in its own juice).
44b: Meat and milk is a Chidush. If one soaks them together they are permitted, but if they are cooked together, they are forbidden.
Rishonim
Rambam (Hilchos Ma'achalos Asuros 9:6): If (meat and milk) were smoked together or cooked in hot spring water of Tiverya, one is not lashed for (eating) it.
Tosfos (Sanhedrin 4b DH Derech): Cooking in Chelev is not called cooking. It is frying, like Rashi says. In Pesachim, we say that Tzeli Kedar is considered Bishul. This is because we learn from a verse.
Ran (43a DH Tanan): The Ri says that even according to the opinion that Chatichah Atzmah Na'asis Nevelah (a piece that became forbidden due to absorptions is considered like pure Isur), it forbids only as far as the Isur itself could have spread. This is why we permit roasting meat (that absorbed Isur) after removing Kedei Kelipah (peeling off a layer). We do not say that the Kelipah becomes Nevelah and forbids the layer under it, and then the next layer...
Rejection (Ran): We learn Chatichah Atzmah Na'asis Nevelah from meat and milk, therefore we apply it only similarly to meat and milk, i.e. through Bishul (cooking in water).A Kelipah does not apply.
Mordechai (Avodah Zarah 827,828): The Gemara permits benefit from cheese curdled in skin of stomachs. This shows that if Basar v'Chalav was forbidden through salting or pickling, only eating it is forbidden, but not Hana'ah. Some reject this. Therefore, we do not protest against one who permits, until there is a proof to forbid.
Rashi (Pesachim 44b DH Taru): The Torah permits to soak meat in milk the entire day and eat it, even if it gives taste. Only Derech Bishul is forbidden. However, mid'Rabanan it is forbidden.
Tosfos (Avodah Zarah 35a DH Mipnei): Shmuel forbids cheese of Nochrim because they curdle in stomachs of Neveilos. Even in a stomach of a slaughtered animal, we should forbid due to Basar v'Chalav! He mentioned the Torah Isur. There is no Torah Isur of Basar v'Chalav here, since both are cold.
R. Akiva Eiger (on Shach YD 87:2): The Mordechai says that since pickling Basar v'Chalav is only mid'Rabanan, it does not forbid Hana'ah. Tosfos asked that meat and milk applies even to slaughtered animals. Why did Shmuel mention Nevelos? Tosfos answered that since pickling is only Basar v'Chalav mid'Rabanan, we are not concerned for a Safek (if he used the skin to curdle, and the meat can be tasted - PF). The Ri mi'Gash and Rambam answered that normally there is 60 times as much milk (as absorptions from the stomach), so there is no taste of meat. We forbid only because it curdled. Curdling does not make Basar v'Chalav. If so, there is no proof to permit Hana'ah from Basar v'Chalav mid'Rabanan. Since the Mordechai disagrees with the other answers, Tosfos' question remains. This requires investigation. Also, the Mordechai's answer, that one may benefit from what was pickled, is difficult. Also according to Tosfos, we should forbid to add cheese of Nochrim to a food and cook it, for if the cheese absorbed taste of meat through pickling, now he transgresses cooking Basar v'Chalav mid'Oraisa and forbids Hana'ah! This requires investigation.
Poskim
Shulchan Aruch (YD 87:1): Three verses say "Lo Sevashel Gedi ba'Chalev Imo." They forbid cooking, eating, and benefit. The Torah used an expression of cooking to forbid eating, to teach that mid'Oraisa it is forbidden only if it was cooked. Mid'Rabanan it is forbidden in every case.
Gra (1): Rashi (104b DH Maskif) says that the Torah forbids only Derech Bishul. This includes anything through fire. He excludes only pickling.
Rema (ibid.): One may benefit from any Basar v'Chalav that is forbidden only mid'Rabanan.
Bach (1): Mid'Rabanan it is forbidden to eat in every case, e.g. even through salting or pickling. One may benefit from it, like it says in 91:8.
Pri Chodosh 87:2): The Torah forbids only Derech Bishul. This includes roasting, like it says "va'Yvashlu ha'Pesach." Also in Beraisos, roasting is called Bishul. It says 'we tear the heart after Bishulo', and we establish (Pesachim 74b) that this refers to roasting. However, the Ran says that it is not mid'Oraisa, therefore Kelipah does not apply. One can reject this. The Ran discussed Stam roasting meat (on which a drop of milk fell). If meat and milk were roasted together, the entire piece is forbidden. Therefore, Kedei Kelipah never applies. Even if you will explain the Ran simply (that the Torah did not forbid even roasting meat and milk together), what I wrote seems primary. We hold that Iruy (pouring from a Kli Rishon) forbids Kedei Kelipah. Surely this is mid'Oraisa, for we hold that Iruy cooks Kedei Kelipah; this is Derech Bishul, even though it forbids only Kedei Kelipah. The Yerushalmi asked about smoking meat (with milk). This implies that it is clear that the Torah forbids roasting. In Pesachim, a verse teaches that Tzli Kedar is considered Bishul. If not for the verse, it would not be considered Bishul! There is different, for the Torah said "Tzli Esh" to exclude roasting. One might have thought that also Tzli Kedar is excluded.
Pri Chodosh: In Sanhedrin, the Gemara suggested that perhaps the Torah forbids cooking meat in Chelev. It rejected this, for the Torah forbids Derech Bishul. Rashi explains that cooking in Chelev is frying. This implies that all the more so, roasting is not Derech Bishul! We can reject this. Granted, if the Torah discusses milk, which is clear, it said 'Bishul', for this is the primary cooking, even though roasting is included. However, if the Torah discusses Chelev, it should not have said 'Bishul', which connotes (cooking in) milk more than (in) Chelev. Indeed, roasting and frying are included in Bishul. The Rambam and Magid Mishneh forbid smoking (meat and milk) due to Safek. This would be unreasonable if the Torah forbids only Derech Bishul (and roasting was excluded). Tosfos in Sanhedrin connotes that pot roast is not considered Bishul regarding meat and milk, and all the more so roasting over a fire. What I wrote is primary. Even though we hold that roasting is like cooking, and salting is like roasting, all agree that they are not considered Bishul. Pesachim 44b explicitly says that the Torah does not forbid picking meat and milk. We learn from pickling to salting, for they are similar.
R. Akiva Eiger (On Sa'if 1): In the Sugya of a drop of milk (that fell on meat), the Ran (43a DH Tanan) says that when Kedei Kelipah is forbidden (one must peel off a layer), we do not say that the entire piece becomes forbidden like a Neveilah. That is only when Basar v'Chalav applies. We never find Kedei Kelipah regarding Basar v'Chalav. However, a drop of milk that falls on roasting meat forbids Kedei Kelipah! The Ran must hold that Basar v'Chalav does not apply mid'Oraisa to roasting. The Pri Chodosh says that roasting, pouring from a Kli Rishon, and putting cold onto hot are mid'Oraisa. The Yam Shel Shlomo (Chulin 3:45) says that if hot meat touched hot cheese, perhaps it is forbidden only mid'Rabanan. Isur v'Heter says that if meat was soaked in milk, one may not cook it. Until now it was forbidden only mid'Rabanan. Cooking it transgresses an Isur mid'Oraisa. This implies that if it was already cooked in milk, one may cook it again.
Shulchan Aruch (91:8): Salting or pickling forbids only eating meat and milk, but one may benefit from it.